# calculus derivative problem help

• Oct 2nd 2012, 10:16 AM
cheshirecat
calculus derivative problem help
Hi, I need help finding the derivative for the problem h(x)= x/2^(1/2) + cos x - 2^(1/2)/2. I think the derivative of cos x is -sin x and -2^(1/2)/2 should be 0 because of the constant rule but what are the steps for the derivative of the first part of the problem? The book I'm using only gives the answer and no explanation. Thank you.
• Oct 2nd 2012, 10:38 AM
MarkFL
Re: calculus derivative problem help
We are given:

$h(x)=\frac{1}{2^{\frac{1}{2}}}x+\cos(x)-\frac{2^{\frac{1}{2}}}{2}$

Differentiate term by term. For the first term use:

$\frac{d}{dx}(kx)=k$

For the second term:

$\frac{d}{dx}(\cos(x))=-\sin(x)$

And for the third term:

$\frac{d}{dx}(k)=0$.

In the above formulas, k is an arbitrary constant.
• Oct 2nd 2012, 10:38 AM
HallsofIvy
Re: calculus derivative problem help
If the function is exactly what you have written then it is the form h(x)= ax+ cos(x)- a with a a constant: $a= \sqrt{2}/2$. Do you know how to differentiate ax+ cos(x)- a?